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Loosely-Stabilizing Leader Election on Arbitrary Graphs in Population Protocols

  • Yuichi Sudo
  • Fukuhito Ooshita
  • Hirotsugu Kakugawa
  • Toshimitsu Masuzawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8878)

Abstract

In the population protocol model Angluin et al. proposed in 2004, there exists no self-stabilizing protocol that solves leader election on complete graphs without knowing the exact number of nodes. To circumvent the impossibility, we previously introduced the concept of loose-stabilization, which relaxes the closure requirement of self-stabilization. A loosely-stabilizing protocol guarantees that starting from any initial configuration a system reaches a loosely-safe configuration, and after that, the system keeps its specification (e.g. the unique leader) not forever, but for a sufficiently long time. Our previous work presented a loosely-stabilizing protocol that solves the leader election on complete graphs using only the upper bound N of n, not the exact value of n. We take this work one step further in this paper: We propose two loosely-stabilizing protocols that solve leader election for arbitrary graphs. One is a deterministic protocol that uses the identifiers of nodes while the other is a probabilistic protocol that works on anonymous networks. Given the upper bounds N and Δ of the number of nodes and the maximum degree of nodes respectively, both protocols keep a unique leader for Ω(Ne N ) expected steps after entering a loosely-safe configuration. The former enters a loosely-safe configuration within O(mΔN logn) expected steps while the latter does within O(mΔ2 N 3logN) expected steps where m is the number of edges of the graph.

Keywords

Loose-stabilization Population protocols Leader election 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Yuichi Sudo
    • 1
    • 2
  • Fukuhito Ooshita
    • 2
  • Hirotsugu Kakugawa
    • 2
  • Toshimitsu Masuzawa
    • 2
  1. 1.NTT Secure Platform LaboratoriesMusashinoJapan
  2. 2.Graduate School of Information Science and TechnologyOsaka UniversitySuita, OsakaJapan

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